Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T06:55:07.673Z Has data issue: false hasContentIssue false

An EM algorithm for mapping binary disease loci: application to fibrosarcoma in a four-way cross mouse family

Published online by Cambridge University Press:  11 November 2003

SHIZHONG XU
Affiliation:
Department of Botany and Plant Sciences, University of California, Riverside, CA 92521, USA
NENGJUN YI
Affiliation:
Department of Botany and Plant Sciences, University of California, Riverside, CA 92521, USA
DAVID BURKE
Affiliation:
Department of Human Genetics, University of Michigan School of Medicine, Ann Arbor, MI 48109, USA
ANDRZEJ GALECKI
Affiliation:
Geriatrics Center, University of Michigan School of Medicine, Ann Arbor, MI 48109, USA Institute of Gerontology, University of Michigan School of Medicine, Ann Arbor, MI 48109, USA
RICHARD A. MILLER
Affiliation:
Geriatrics Center, University of Michigan School of Medicine, Ann Arbor, MI 48109, USA Institute of Gerontology, University of Michigan School of Medicine, Ann Arbor, MI 48109, USA Department of Pathology, University of Michigan School of Medicine, Ann Arbor, MI 48109, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Many diseases show dichotomous phenotypic variation but do not follow a simple Mendelian pattern of inheritance. Variances of these binary diseases are presumably controlled by multiple loci and environmental variants. A least-squares method has been developed for mapping such complex disease loci by treating the binary phenotypes (0 and 1) as if they were continuous. However, the least-squares method is not recommended because of its ad hoc nature. Maximum Likelihood (ML) and Bayesian methods have also been developed for binary disease mapping by incorporating the discrete nature of the phenotypic distribution. In the ML analysis, the likelihood function is usually maximized using some complicated maximization algorithms (e.g. the Newton–Raphson or the simplex algorithm). Under the threshold model of binary disease, we develop an Expectation Maximization (EM) algorithm to solve for the maximum likelihood estimates (MLEs). The new EM algorithm is developed by treating both the unobserved genotype and the disease liability as missing values. As a result, the EM iteration equations have the same form as the normal equation system in linear regression. The EM algorithm is further modified to take into account sexual dimorphism in the linkage maps. Applying the EM-implemented ML method to a four-way-cross mouse family, we detected two regions on the fourth chromosome that have evidence of QTLs controlling the segregation of fibrosarcoma, a form of connective tissue cancer. The two QTLs explain 50–60% of the variance in the disease liability. We also applied a Bayesian method previously developed (modified to take into account sex-specific maps) to this data set and detected one additional QTL on chromosome 13 that explains another 26% of the variance of the disease liability. All the QTLs detected primarily show dominance effects.

Type
Research Article
Copyright
© 2003 Cambridge University Press